1. FORCES

2. Pulleys and Tension
To understand and correctly use the terms “pulley” and “tension.” To set up and solve word problems involving pulleys and/or tension.

3. Tension The pulling force exerted on a rope, cable, etc.
(Symbol: T, FT).

4. Pulley
A wheel used to change the direction of tension on a rope.

5. Problems with Pulleys
Find the acceleration of blocks m1 and m2. (Assume that the pulley has negligible mass and the surface and pulley are frictionless.)

6. Free-body Diagrams for the Two Masses
FN FT FT
Fg Fg

7. Therefore FT ia the net force on m1. For m1, Fnet= m1a
For m2, gravity and tension are pulling in opposite directions. The net force is therefore Fnet= Fg- FT = m2a
The blocks are connected so, FT and a are the same for both blocks.

8. Sample Problem 1 Suppose we had the following situation:
Calculate the acceleration of the pair of blocks.
5 kg
2 kg

9. Youtube Video How to solve pulley problems in physics
(AP Problems may not have values)

10. Answer For the block on the table:
Fnet= FT = m1a = (5)(a) = 5a
For the block hanging from the pulley:
Fnet= Fg- FT = m2a = (2)(a)
(2)(10) - FT = 2a
20 - FT = 2a
Substitute FT = 5a into the second equation.
20 - 5a = 2a
20 = 7a
a = 20/7 = 2.9 m/s2

11. Sample Problem 2
Two masses, m and M, are connected by an ideal (massless) rope over an ideal pulley (massless and frictionless). What is the acceleration of the larger mass, in terms of m, M, and g?
m1 is m and m2 is M

12. Solution Substitute (2) in (1) Mg - (ma + mg) = Ma Mg - ma - mg = Ma
Mg - mg = Ma + ma
g(M - m) = a(M + m)
(M + m) (M + m)
Solution
For mass, M:
Fnet = Fg - T = Ma
= Mg - T = Ma (1)
For mass, m:
Fnet = T - Fg = ma
= T - mg = ma
T = ma + mg (2)

13. Atwood’s Machine AP Physics Atwood Machine

14. Classwork/ Homework
Complete the Pulleys and Tension Worksheet

15. Friction
To calculate the frictional force on an object and to calculate net force in problems involving friction.

16. Demo
Drag a heavy object attached to a spring scale.

17. Friction
It is a contact force caused by the roughness of the materials in contact, deformations in the materials, and molecular attractions between materials.
Frictional forces are always parallel to the plane of contact between two surfaces, and opposite to the direction of motion or applied force.

18. Static Friction
The friction acting on an object at rest that resists its ability to start moving.
Push or pull is not large enough to move the object.

19. Kinetic Friction